1. **State the problem:** We need to estimate the number of rings containing between 1.4 g and 3 g of gold using the histogram data. 2. **Recall the formula for frequency:** The frequency for a class interval in a histogram is given by: $$\text{Frequency} = \text{Frequency density} \times \text{Class width}$$ 3. **Identify relevant intervals and frequency densities:** - From 1 to 2 g, frequency density = 25 - From 2 to 2.5 g, frequency density = 50 - From 2.5 to 3 g, frequency density = 30 4. **Calculate frequencies for parts of the range 1.4 to 3 g:** - For 1.4 to 2 g (part of 1 to 2 g interval): Class width = $2 - 1.4 = 0.6$ Frequency = $25 \times 0.6 = 15$ - For 2 to 2.5 g: Class width = $2.5 - 2 = 0.5$ Frequency = $50 \times 0.5 = 25$ - For 2.5 to 3 g: Class width = $3 - 2.5 = 0.5$ Frequency = $30 \times 0.5 = 15$ 5. **Add frequencies to estimate total number of rings between 1.4 g and 3 g:** $$15 + 25 + 15 = 55$$ 6. **Answer for part a):** The estimated number of rings containing between 1.4 g and 3 g of gold is 55. 7. **Answer for part b):** This is only an estimate because the histogram groups data into intervals and assumes uniform distribution of frequency density within each interval, which may not be exactly true. Also, the exact number of rings is not given, only frequency densities.